Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x + 9$ and $ KL = 8x + 5$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x + 9} = {8x + 5}$ Solve for $x$ $ -x = -4$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({4}) + 9$ $ KL = 8({4}) + 5$ $ JK = 28 + 9$ $ KL = 32 + 5$ $ JK = 37$ $ KL = 37$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {37} + {37}$ $ JL = 74$